Anti-Specker Properties in Constructive Reverse Mathematics
| dc.contributor.author | Dent, James Edgar | |
| dc.date.accessioned | 2014-05-05T01:59:02Z | |
| dc.date.available | 2014-05-05T01:59:02Z | |
| dc.date.issued | 2013 | en |
| dc.description.abstract | Constructive reverse mathematics is a programme in which non- and semi-constructive principles are classified in accordance with which other principles they imply or are implied by, relative to the framework of Bishop-style constructive mathematics. One such principle that has come under focus in recent years is an antithesis of Specker's theorem (that theorem being a characteristic result of Russian recursive mathematics): this so-called anti-Specker property is intuitionistically valid, and of considerable utility in proving results of real and complex analysis. We introduce several new weakenings of the anti-Specker property and explore their role in constructive reverse mathematics, identifying implication relationships that they stand in to other notable principles. These include, but are not limited to: variations upon Brouwer's fan theorem, certain compactness properties, and so-called zero-stability properties. We also give similar classification results for principles arising directly from Specker's theorem itself, and present new, direct proofs of related fan-theoretic results. We investigate how anti-Specker properties, alongside power-series-based arguments, enable us to recover information about the structure of holomorphic functions: in particular, they allow us to streamline a sequence of maximum-modulus theorems. | en |
| dc.identifier.uri | http://hdl.handle.net/10092/9169 | |
| dc.identifier.uri | http://dx.doi.org/10.26021/3462 | |
| dc.language.iso | en | |
| dc.publisher | University of Canterbury. Department of Mathematics and Statistics | en |
| dc.relation.isreferencedby | NZCU | en |
| dc.rights | Copyright James Edgar Dent | en |
| dc.rights.uri | https://canterbury.libguides.com/rights/theses | en |
| dc.subject | anti-Specker property | en |
| dc.subject | constructive mathematics | en |
| dc.subject | constructive reverse mathematics | en |
| dc.subject | fan theorem | en |
| dc.subject | holomorphy | en |
| dc.subject | maximum-modulus theorem | en |
| dc.subject | power series | en |
| dc.subject | zero-stability | en |
| dc.title | Anti-Specker Properties in Constructive Reverse Mathematics | en |
| dc.type | Theses / Dissertations | |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | University of Canterbury | en |
| thesis.degree.level | Doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |
| uc.bibnumber | 2002958 | en |
| uc.college | Faculty of Engineering | en |